parilla



y 1963 A. R. PARILLA 3,096,576

FABRICATION OF BODIES HAVING COMPOUND CURVATURE Filed Sept. 24, 1958 5Sheets-Sheet 1 INVENTOR.

ARTHUR R. PARILLA /7 MORGAN, FINNEGAN, DURHAM 8 PINE ii 20 ATTORNEYSJuly 9, 1963 A. R. PARILLA 3,095,575

FABRICATION OF BODIES HAVING COMPOUND CURVATURE Filed Sept. 24, 1958 3Sheets-Sheet 2 FlG.-3

INVENTOR.

ARTHUR R. PARILLA BY IMORGAN, FINNEGAN, DURHAM a PINE ATTORNEYSFABRICATION OF BODIES HAVING COMPOUND CURVATURE Filed Sept. 24, 1958 A.R. PARlLLA July 9, 1963 3 Sheets-Sheet 5 L P Rm 0 a T P W W D ATTORNEYSUnited States Patent 3,096,576 FABRICATION 0F BODIES HAVING COMPOUNDCURVATURE Arthur R. Parilla, 34 Crestview Road, Mountain Lakes, NJ.Filed Sept. 24, 1958, Ser. No. 763,114 17 Claims. (Cl. 29-421) Thisinvention relates to new and improved methods for fabricating bodieshaving compound curvature. It is more specifically related to improvedmeans for fabricating thin wall semi-elliptical and/or hemi-spher-icalhead closures of high quality for use in ultra light weight, highlystressed pressure vessels, such as solid propellant rocket cases and/ orfuel tanks for missile use.

Such bodies have curvature in two or more planes and require extensiveplastic flow of the material in order to form the desired shape, whereasbodies such as cylinders and cones having curvature in one plane onlycan be readily formed by rolling a flat sheet.

It is, therefore, the primary purpose of this invention to provide novelmethods for forming bodies having compound curvature by first formingsimple bodies having curvature in one plane only and then subsequentlyproducing curvature in the second plane also.

Semi-elliptical and/or hemi-spherical heads may be readily formed bypresent fabrication methods such as deep-drawing or spinning when madein thick wall sections and using low alloy steels having goodformability with high ductility, low yield strength and lowworkhardening characteristics. The resulting structure, how-. ever, istoo heavy for missile application. These require very thin walledstructures using more difficult to form ultra high strength steel alloysof higher carbon content, relatively low ductility, higher yieldstrength and higher work-hardening properties. In addition, theprecision requirements are more severe; excessive local thinning of themetal during forming cannot be accepted because of the low margins ofsafety employed to achieve the weight reduction essential to missileperformance.

As an example, the minimum wall thickness for a 54 inch diameter headwhich can now be economically fabricatecl commercially with the easierto form low alloy steels, is inch for elliptical heads and inch forhemi-spherical heads. In contrast, the requirements for missileapplication are for thicknesses of only 0.078 inch for the same diameterwhile using the more difficult to form super alloys such as tool steels,hot work die steels, or modifications of 4340 alloy steels, titaniumalloys, magnesium alloys, and the like.

A major difficulty with deep-drawing such head closures is due to thehigh compressive stresses induced in the circumferential direction asthe flat metal blank is drawn into the die. These compressive stressesrequire high radial tensile stresses, the combined effect being to thinthe metal near the bottom of the die and thicken the metal near the topof the die. This leads to wide variation in wall thickness along anymeridian.

The compressive stresses cause lateral buckling or wrinkling of theblank, this tendency to buckle increasing as the wall thicknessdecreases and diameter increases,

being a function of the second power of the ratio of diameter to wallthickness, thus aggravating the problem with thin wall structures.Hold-down fixtures or pressure plates are used on the blank to restrainbuckling; this increases radial tensile stresses in the blank, sometimescausing tearing of the metal, while the application of pressureincreases the capacity of the press required. Also, this requires alarger diameter blank, leaving a flange normal to the axis of the headwhich must be trimmed later; and aggravates the forming operation sincethe larger blank diameter again increases the percent of de- 3,096,576Patented July 9, 1963 2 formation required to form the part, againincreasing press capacity requirements.

While heads formed by spinning a flat sheet blank over a suitablemandrel of the desired curvature, is an alternate method successfullyused in heavy wall, ductile material, it is unsatisfactory in thingages. This method causes excessive thinning of the metal, requiring useof heavier stock in order to maintain the minimum wall, thus resultingin considerable variation in wall thickness along any meridian. Thehigher alloy material also work-hardened during the excessivedeformation required to produce the final article.

Another fabrication method sometimes used is to form the segments of thehead to the desired contour, then weld such segments into a unitizedstructure. This requires elaborate jigs and fixtures to position thesegments, and high quality welding techniques to insure sound joints,leading to expensive fabrication including weld X-ray and other qualitycontrol techniques; it lacks reliability since even slight mis-match oreccentricities at welded joints can induce high stress raisers beyondthe nominal membrane stresses for which the structure is usuallydesigned.

In any of the above methods, the normal commercial tolerances on wallthickness of the original sheet as rolled causes further variation inthickness and hence weight of the completed part. This variation inweight from unit to unit in production is objectionable as it affectsthe reproducibility of performance of the complete missile.

When such head closures are used for solid rocket propellant cases,there is generally a requirement for central openings in such heads. Theforward head generally requires a relatively small opening forattachment of an igniter flange; the aft head closure requires asubstantial opening for a nozzle attachment flange. Present fabricationmethods require forming the complete head and then removing portions forthe required openings. Such methods do not utilize the advantage whichmay be taken of such openings to facilitate fabrication. An annularsurface is all that is required in the final product.

It is, therefore, a primary object of this invention to provide novelfabrication methods for bodies having compound curvature which may bespecifically adapted to produce thin walled bodies.

It is a further object of this invention to provide novel means forfabricating such bodies in which the material is subject to tensilestresses only, thus eliminating the difficult forming operations whenhigh compressive stresses are induced, such as by deep-drawing.

Another object is to reduce the strain or percent of deformationrequired to form bodies having compound curvature by taking advantage ofthe need for central openings, and forming only the annular compoundsur-' face.

Another object is to provide novel fabrication methods for bodies havingcompound curvature in which a uniform wall thickness may be maintainedwith close tolerances along any meridian.

Another object is to provide simple and flexible means whereby suchbodies may be readily formed without the need for high capacity presses,such as by fluid forming or explosive forming; and in which designchanges may be readily incorporated with a minimum of lead time.

Another object is to reduce the press capacity require ments for pressforming such bodies in large quantities and at low cost, and of superiorquality.

Another object is to provide means for fabricating such bodies whichlimit the amount of deflection occurring under tension to the ductilitylimits of the material.

The basic principles of this invention may be defined by the followingfurther objects in which:

Another object is to fabricate bodies having compound a curvature, suchas semi-elliptical or hemi-spherical heads, by first making a pre-formcomprising a body having curvature in one plane only and thus may beeasily rolled from fiat sheet, the pre-form approximating the finalcompound curvature only. The pre-form may then be inserted Within a diehaving a contour of the final desired shape. The pre-form is thenstretched or expanded to the shape of the die contour to provide thedesired curvature in the second plane. Since the metal in the pro-formis subjected only to .tensile stresses during forming, buckling orwrinkling due to high compressive stresses are eliminated.

Another object is to select the shape of the pre-form so that the amountof deformation or percent elongation during subsequent forming will beminimum, thus minimizing variation in wall thickness in the finalarticle.

Another object is to vary the wall thickness of the preform so that thefinal part as formed will have a constant and uniform wall thicknessalong any meridian. Thus, the variable wall thickness in the pre-formanticipates the reduction in thickness due to Poissons ratio resultingfrom elongation of the material while stretching or expanding thepre-form.

A further object is to vary the wall thickness of the pre-form so thatthe final formed part may have a tapered or variable Wall thicknesswhich varies along any meridian in any prescribed manner to suit designrequirements; the variable wall thickness in the pre-form nowanticipating both the eifect of Poissons ratio and the desired finalthickness.

These and other objects will become apparent from the following detaileddescription read in connection with the annexed drawings, in whichsimilar reference characters represent similar parts, and in which:

FIGURE 1 shows one embodiment of a method for forming a body havingcompound curvature which is approximately semi-elliptical in crosssection.

FIGURE 2 shows a modification of FIGURE 1 whereby the body isapproximately hemi-spherical in cross-section.

FIGURE 3 shows a method for providing constant wall thickness along anymeridian in the final formed part.

FIGURE 4 shows a method whereby the final formed part may have a wallthickness along any meridian which may be tapered or varied in anymanner to suit design requirements.

FIGURE 5 is a fragmentary view showing a detail of the forming operationoccurring in either FIGURE 1 or 2.

FIGURE 6 shows an alternate method for assembly of components of FIGS. 1and 2.

FIGURE 7 shows still another method of components of FIGS. 1 and 2.

FIGURE 8 shows a method for reducing the press capacity for formingthin-walled bodies having compound curvature with superior quality andlow cost.

FIGURE 9 shows a method for fabricating light weight hemi-sphericalheads with integral re-inforcement flanges.

Referring to FIGURE 1, two pro-forms 10 having a frusto-conieal shapeare assembled within identical opposed dies 11, joined by the bolts 12along the flanges 13. A rubber ring, 14, forms a seal between the bases36 of the two cones and the dies 11. Two rubber discs 15 provide a sealbetween the upper cone ends 16 and the dies 11. A nut 17 providesinitial compression of the rubber disc 15 by means of threads on thetube 18 and the cap 19. Fluid pressure admitted through the tube 18 bythe valve 33 causes the pre-form to deflect until it reaches the wall ofthe disc 11 as shown by the dashed lines at 16'.

An alternate method for pressurizing the pre-form is also shown inFIGURE 1 wherein the nut 21 provides initial compression of the rubberdisc 15 by means of threads on the tube 22 and the cap 23. Wires 24 and2.5 are sealed and insulated within the tube 22 and connected to anexplosive charge 26 mounted within the pro-form. When the wires 24 andare energized electrically from for assembly any external source, suchas a battery (not shown), the gaseous products of combustion exertsufiicient pressure to deflect the walls of the pre-forms 10 until theyreach the Walls of the dies 11 as shown by the dashed lines 10', andpreviously described. The valve 33 may then be used to release thepressure after forming. In either case, vents 34 are provided throughthe dies 11 to relieve the back pressure as the pre-form deflectsagainst the dies 11.

It is understood that both methods of pressurization described above areshown in FIGURE 1 for illustrative purposes, but only one or the othermethod would be used as desired. The explosive charge method, whilerequiring greater development, is desirable since it causes a more rapidrate of loading, and also minimizes sealing problems.

It is also understood that any method of stretching the pre-form may beused, such as by insertion of a die within the pro-form, as describedlater, the pre-form replacing the flat sheet in the present pressoperation, the pre-form avoiding the buckling and wrinkling problemspresently encountered by this method. The use of two opposed dies withfluid pressurization of the pre-form eliminates the need for largecapacity presses and costly matched dies.

Since the opposed dies 11 for housing the pre-forms are heavily walledheads, they may be fabricated by present methods. The internal contourmay be machined to various odd dimensions required for any application,while the dies are formed to standard dimensions available from existingtools. Design changes may thus be readily executed with a minimum oflead time. The machined contour of the internal surface of the dies 11may also provide for spring-back allowance.

FIGURE 2 illustrates the same principles of FIGURE 1, the same numeralsreferring to the same functional parts, and shows suitable modificationsfor forming a hemi-spherical instead of semi-elliptical heads.

In forming hemi-spherical heads, the required total elongation in thepro-form material is substantially greater than in formingsemi-elliptical heads and may Well exceed the allowable elongationpermitted by the ductility of the material. This total elongation,however, may be split up into any number of progressive operations, eachone of which controls the elongation well within the allowable limits ofthe material; intermediate annealing operations are then used betweensuccessive forming operations.

As illustrated in FIGURE 2, the elongation in any one operation islimited by spacers 31 fitted within the die 11. The spacers may be ofany of the new plastic die materials, such as the epoxy resins, and castwithin the die 11. As an example, the pre-form 19 may first bepressurized until its deflection engages the inner contour of the spacer31 as shown by the dashed lines at 10. The spacer may then be removed,and after an intermediate anneal of the pre-form 10', re-pressurizationwill cause the pre-form to reach its final position as shown by thedashed lines 10".

The number of progressive operations may be determined by the geometryand property of materials to be used; also, it may be desirable toeliminate spacers and use integral intermediate dies having the desiredinternal contour.

FIGURE 3 illustrates in exaggerated form the modification to thepre-form of FIGURE 2 to provide for a constant and uniform wallthickness along any meridian. It is a well known property of materialsthat elongation in one plane will produce contraction in another planenormal to the first plane; the ratio of this contraction to elongationbeing known as Poissons ratio. If the pro-form is of constant thickness,it will have a minimum thickness where the elongation in thecircumferential direction is maximum. Although the total elongation, andhence thinning, will be less than that occurring when forming the partfrom a flat sheet, this thinning may be anticipated and eliminatedentirely by providing a variable wall thickness in the pre-formproportional to the elongation occurring ateach increment of length, asshown in FIG- URE 3.

An extension of this same principle is illustrated in FIGURE 4. The wallthickness of the pre-form may vary so as to intentionally introduce anydesired variation in wall thickness of the final article after forming.While the illustration shows an increased wall thickness as thespherical head approaches the centerline, it is readily apparent that areverse taper of the pre-form wall would produce a spherical head havinga thicker flange portion.

The change in wall thickness resulting from the effect of Poissons ratioas the pre-forrn is expanded to the die contour may be readilycalculated from the following relation:

where e is the strain or percent change in wall thickness; (I is thenormal stress in the wall; E is the modulus of elasticity of thematerial; ,u. is Poissons ratio, :030 for steel; s is the strain in thematerial in a circumferential direction; and q is the strain in thematerial in a longitudinal direction or along the slant height of thepre-form.

Since o' is numerically equal to the pressure acting on the case, it isvery small with respect to E, and the first term may be assumed equal tozero.

For the assemblies shown in FIGURES -l and 2, the ends 36 of thepre-form are unrestrained and therefore may move freely in a directiontowards the cone apex during the forming operation. The seal 14 hassuflicient length and flexibility to maintain engagement with thepreform as this movement progresses. Neglecting small elastic strain,the value of 6 is also zero with no end restraint. The above relationfor calculating change in wall thickness reduces to:

. 11' c a may be readily calculated by determining the loci of a numberof points on the conical pre-form as deflection occurs, the upper orsmall diameter of the pre-form 16 reinaining in fixed position relativeto the die 11. 6 is then found from Ru (3) where R is the final radiusof any circumferential element andR is its initial radius on the cone.

From the above relations the contour or the pre-forrn for FIGURE 3 maybe readily calculated. This increment may then be added to any desiredtaper or variation in Wall thickness desired by the designer, forexample as shown in FIGURE 4.

' Referring to FIGURES l and 2, when the end 36 of the pre-form 10 is inclose engagement with the wall of the die 11, the available local strainin this region may not exceed the yield point of the material. 'CNoplastic deformation will occur and the local deflection of the preformin this area is then illustrated in exaggerated form by FIGURE 5. Thematerial over a small length, such as L of FIGURE 5 will then bestressed only elastically, with a gap as at 37 remaining afterde-pressurization.

The length, L, is related to the thickness of the wall, h, of thepre-form by the following approximate expression:

where 0,, is the yield stress of the material, P is the maxi mumpressure acting on the pro-form.

For high strength steel alloys having a yield strength of 90,000 p.s.i.,and for a maximum working pressure of 2,000 p.s.i., the length L will beapproximately 7 .7h; and for h: 0.07 8, (typical) L is approximately 0.6inch.

For the above case, the maximum gap at 37 will then be approximately0.003 inch, resulting in an eccentricity of 3.8% of the wall thickness.In the event the margin 6 p of safety (allowable stress over actualstress) exceeds this amount, the end would not require trimming; if themargin of safety is less than this amount, the end should be trimmed ator above L, or higher pressure used.

The same type deflection curve will occur at the upper end of thepre-form at 16.

In the assembly shown in FIGURE 6, sufiicient clearance as at 34 may beallowed between the pre-form end 36 and the die 11 in the design of thepre-form so that the base 36 will exceed the elastic limit of thematerial before reaching the die wall. The seal .14 is modified to beardirectly on the die between pre-forms. The upper end of the pre-form at16 will continue to deflect in the manner illustrated by FIGURE 5.

Other modifications illustrated in FIGURE 6 include alternate methodsfor assembling the various components. The bolts '12 of FIGURES l and 2may be replaced by two Ortrnan keys 32 which mate with suitable groovesin the dies 11 and in similar grooves in the continuous ring 38.Assembly and dis-assembly may be facilitated, it being necessary toremove only one of either of the two Ortman keys 32 in a manner wellknown in the art, to effect dis-assembly.

A plate 35, centered on the tube 22, or integrally machined as part ofdie 11, provides concentricity for the pre-form 10 relative to the die11 and offers positive positioning of the upper or small end 16 of thepre-form 10, a similar arrangement (not shown) being used for theopposed pre-form and die at the opposite end.

FIGURE 7 illustrates another method of assembly in which the bases 36 ofthe opopsed pre-forms 10 are welded together, eliminating the seal ringM, the weld being performed after the seals 15, explosive charge 26 (ifused) and associated components have been pre-assembled Within thepre-form. After forming, the parts are separated by cutting above andbelow the weld, such as by the distance L shown in FIGURE 5.

When this method is used, the variation in Wall thickness will begreater as determined by Equation 1 since the longitudinal strain, 5 isno longer Zero when the end 36 is restrained. This will require greatercamber for the initial wall thickness of the pre-forrn of FIGURE 3 or 4.It will provide a longer straight flange on the formed part, orconversely a shorter pre-form may be used when longitudinal endrestraint is applied as shown.

Another method for stretching the pre-form to its final compoundcurvature is shown in FIGURE 8. In this case, the part may be pressformed by a novel method in which the press capacity required may besubstantially reduced compared to deep drawing, cold forming, or othermeans, as described later. Simple. dies may be used, eliminatinghold-down fixtures or pressure plates required for deep drawing.

Referring to FIGURE 8, a female die 41 is formed to have the desiredcontour as at 42, a portion of a semielliptical contour being shown. Thedie 41 has an integral land 43 corresponding to the diameter of thecentral opening, or the land may be formed by a separate plate, such asshown by 35 in FIGURE 6. The pre-form v10 is inserted in the die 41 withits small diameter 16 abutting on the land 43. The male die 44 has acontour 45 matched to the contour 42 of the female die with clearancefor the metal thickness of the pre-form 10. A recess 46 in the male die44 provides clearance for the land 43 of the female die, when in closedposit-ion. When the dies are closed, the conicalpre-form is stretchedinto the compound curvature of the die, as shown at 10'.

The press capacity is reduced for a number of reasons as follows:

(.1) Advantage is taken of the fact that the finished part frequentlyhas a sizable opening or hole on its axis; present practice is to form acontinuous head, then re move a portion from the completely formed part.By the method shown in FIGURE 8, only the annular surface remaining inthe final article requires forming.

(2) The metal to be formed is already within the die and subject totensile stresses only, requiring only moderate pressure on the pre-form.It is not necessary to overcome large compressive stresses in a blank asthe material is drawn into the die as occurs in the deep draw operation;no hold down pressures are required to resist buckling or wrinkling,since the compressive stresses inducing this condition have beenremoved.

(3) Since the magnitude of the pressure required on the pre-forrn isless than that required on the continuous flat sheet in a deep draw, andsince this reduced pressure also acts on the reduced area of only theannular surface being formed, it follows that much smaller presscapacity is required compared to other processes.

FIGURE 9 shows modifications to the die 11 of FIG- UR-E 2 and thepre-form 10 of FIGURE 4, especially adapted to fabricate hemi-sphericalhead closures of minimum weight, other components being as shownpreviously.

It is well known by those familiar with the art that the membrane stressin hemi-spherical head closures is nominally one-half the tangentialstress in the cylindrical portion of a pressure vessel. The wallthickness of the hemispherical head may then theoretically be one-halfthe wall thickness in the cylindrical portion. It is generally difiicultto achieve this in practice, since the straight flange portion of thehead forms part of the cylindrical chamber and therefore requires thefull thickness of the cylindrical wall. Also, it becomes more difiicultto perform the welding operation with dissimilar thickness increasingthe risk of misalignment or mismatch, the result of such localeccentricities inducing high stress raisers which far exceed the nominalmembrane stresses.

As shown in FIGURE 9, the frusto-conical pre-form may be fabricated tohave an enlarged section 47 at its base, joined by a gradual transitionsection 48 to a thin section 49, which may be cambered to compensate foreffect of Poissons ratio, as described previously, or have parallelwalls, in either case providing a much reduced thickness of up to 50%compared with hemi-spherical heads of constant wall thickness.

A similar construction of the pre-form is shown at the small diameteropening at 50 to provide local re-inforcement for the connectingstructure.

Both end re-inforcements at 47 and 50 are symmetrically disposed aboutthe centerline to insure local eccentricities will not be present in thecompleted structure.

The normally spherical internal contour of the die 11 is modified byproviding recesses at 51 and 52 to receive the re-inforced ends 47 and50 of the pre-form, thereby again insuring concentricity of all sectionsof the completed structure.

Other features of the process, such as progressive forming withintermediate annealing, use of seals, etc., may be as previouslydescribed.

While the description and drawings show head closures having centralopenings, it can be seen that this process may be readily adapted toform closed surfaces. The major portion of the forming operation may beperformed as described, with the central opening at the upper end of thefrusto-conical pre-form reduced to a small diameter. Since connectingfittings are usually required, the small opening may be designed toreceive a standard flange for such connections; or a spherically formedsegment sometimes described as a dollar-plate, may be welded orotherwise attached to close the opening of the conical preform.

While this process is described to form head closures for cylindricalpressure vessels, such as rocket cases with reference to ultra highstrength steel alloys, it is obvious it may also ofiier improvement forfabrication of other bodies of other materials, such as fuel tanks formissiles, accumulators of titanium, and the like. Nor need it be limitedto semi-elliptical or hemi-spherical bodies; it may also be applied tovarious ogival shapes for missiles, contoured or hell shaped nozzles forsuper-sonic jets,

8 engine cowling, and a variety of parts having compound curvature.

Having now described the basic principles and theory of a novelfabrication method for forming thin walled bodies having compoundcurvature, together with various methods for performing the operations,the actual fabrication of a typical head closure will now be describedwith application of these principles.

Two semi-elliptical head closures will first be considered for use withsolid propellant rocket cases.

(A) An aft head closure for a 54 inch diameter case with an 0.078 inchwall thickness and having a relatively large central opening of 75% ofthe case diameter (40.5 inches) for attachment of a nozzle assembly.

(B) A forward head closure also 54 inches in diameter by 0.078 inch wallthickness, having a relatively small central opening of 25% of the casediameter (13.5 inches).

In both cases a straight flange of two inches is assumed for the finalformed part; and the forming operation will be without end restraint, asillustrated in FIGURE 1 or FIGURE 8.

For head (A), the large central opening results in a frusto-conicalpre-form with a relatively small apex angle so that the maximumcircumferential elongation during forming is approximately 9%. UsingEquation 2, the wall thickness will reduce a maximum of 2.7%, or by0.0021 inch; the minimum wall thickness becomes approximately 0.076inch. Obviously, a flat sheet may be used for the pre-form withoutcamber since there is little thinning of the metal.

For head (B), the smaller central opening results in a frusto-conicalpre-form having a larger apex angle so that the maximum circumferentialelongation becomes approximately 20%. Again using Equation 2, the wallthickness will reduce approximately 6%, or by 0.0047 inch; the minimumwall thickness becoming 0.073 inch. Again, a fiat sheet may be used forthe pre-form without camber with less than 0.005 inch maximum variationin wall thickness due to forming.

It may thus be seen that semi-elliptical head closures of high qualitymay be fabricated in thin sections by this method, with only slightvariation in wall thickness due to forming.

As case diameter and wall thickness increase, the same percent variationwill cause a larger absolute tolerance requirement on the finished part;cambered walls may then be used to maintain closer tolerances ifrequired.

The low value of 9% circumferential elongation for head (A) above maypermit forming this head in a single operation without intermediateanneal, even with workhardening steels.

For comparison of hemi-spherical heads with semielliptical heads, it isassumed that head (B) above has a hemi-spherical shape; the maximumcircumferential elongation, using a frusto-conical pre-form with no endrestraint, then increases to approximately 30%; using Equation 2, thevariation in wall thickness becomes 9%, or 50% greater than for thesemi-elliptical head. For an 0.078 inch wall, the thickness reduces by0.0072 inch; the minimum wall becomes approximately 0.071 inch. Thisoccurs in the hemi-spherical section where the stress is nominallyone-half of the tangential stress in the cylindrical case.

The maximum circumferential elongation in the hemispherical head fiangeportion is only 4.5% resulting in a thickness reduction of only 1.35%;for an 0.078 inch Wall, the flange thickness will reduce only slightlymore than 0.001 inch. A pre-form of flat sheet without camber may alsobe used for a hemi-spherical head in this diameter and thickness;however, the minimum weight for such a head would be achieved by thedesign and method described above in connection with FIGURE 9.

The design and fabrication of the pre form may now be described:

Since the frusto-conical pre-form has curvature in only one plane, itmay readily be rolled from flat sheet. It either may be rolled andwelded, in which case at least one longi-tudinal weld will be requiredalong the slant height; or it may be roll-formed by *Hydrospinning orFlo-turning, in which case a weldless pre-lform can be made.

The large end, or base diameter of the preform, may be approximately thesame as the shell diameter of the pressure vessel or rocket case; or, inthe event it is desired to eliminate the small local eccentricity asdiscussed in connection with FIGURE 5, it may be made approximately 0.5%smaller than the shell diameter.

The upper diameter or small end of the frusto-com'cal preform is madeequal to the central opening required in the finished piece, less anytrimming allowance, if required.

For closed heads, this opening may be made as small as convenient forattachment of a dollar plate or standard fitting as required, andpreviously described.

The length of the pre-forrn is determined from the depth of headrequired, i.e. semi-elliptical or hemispherical; and is taken as theperimeter of the formed part from the central opening to the tangentpoint, plus the length of the straight flange, plus a trimmingallowance, if required.

For rolled and welded pre-forms, the Weld overlay may be ground flush atleast on its outer surface, with usual quality controls, such as X-rayinspection, to insure sound welds.

The use of hydrospun frusto-conicalpre-forms offers a more economicaluse of hydrospin machines since the cones can be rolled more quickly andless expensively from sheet metal, compared to rolling semi-ellipsoidalor hemi-spherical shapes; the cones may then be readily converted intothe more difiicult shapes by stretching in the manner described herein,thereby increasing the productive capacity of the hydrospin machine.

With either the rolled and welded or hydrospun preforms, the materialwould be soft annealed for maximum ductility.

When extremely close tolerances are required on the final part, thepro-form may be machined to final dimensions thus eliminating variationin wall thickness due to commercial tolerances on light gages; whenrequired, the desired camber may be provided, as by tracer attachment onthe lathe or hydrospin machine.

Thus, novel fabrication methods have been described which make possiblethe fabrication of bodies having compound curvature, particularlyadaptable to thin wall structures and materials difficult to form byknown methods; and can produce an article of superior quality. Whileseveral embodiments and arrangements of my invention have beendescribed, it is understood that changes and modifications may be madetherein without departing from the spirit and scope of the invention.The limits of the invention are set forth in the following claims.

I claim:

1. The method for forming a desired thin-walled body of compoundcurvature from a flat body of hard-to-work thin sheet metal, whichmethod comprises: deforming said flat sheet metal body into a curvedpreform body approximately the shape of the desired body of compoundcurvature and having a curvature in only one of at least two sets oftransverse parallel planes; inserting said preform body into a diehaving a shaped curved surface corresponding to the shape of the desiredbody of compound curvature; sealing the joint between said preform bodyand said die; and then deforming said curved preform body into thedesired thin-walled body of compound curvature, by expanding by fluidpressure said curved preform body in the set of planes of its originalcurvature only, to impart curvature in said curved preform body in theother of said sets, until said body conforms to said shaped curvedsurface.

2. The method as defined in claim 1 characterized by expanding thematerial of the preform in the set of planes of its original curvatureonly, and providing freedom of motion for displacement of the materialof the preform in the other of said sets.

3. The method as defined in claim 1, in which the expanding force isapplied through an incompressible fluid.

4. The method as defined in claim 1, in which the expanding force isapplied through a fluid which comprises the gaseous products ofcombustion derived from an explosive charge.

5. The method for forming bodies having curvature in at least two planeswhich comprises forming a flat body into a preform body approximating afrustum of a cone in shape, inserting the frusto-conical preform into adie having a shaped surface generated by the rotation of a curved lineabout the central axis of said die, said preform being positioned withits apex encircling the central axis of said die and held fixed relativethereto, sealing the joint between said apex and said die, the base endof said frusto-conical body being positioned adjacent the shaped surfaceof said die and movable relative thereto, sealing the joint between saidbase and said shaped surface, closing the base of said die andincreasing fluid pressure within said frusto-conical preform body tostretch the material thereof to engage the shaped surface of said die.

6. A die including a shaped surface generated by the rotation of acurved line about the central axis of said die, a preform body, holdingmeans on said die and at the central axis thereof adapted to engage theapex of a generally frusto-conically shaped preform body to hold saidbody fixed in position relative to said die and to seal the space withinsaid frusto-conical body from the space external thereof at said holdingmeans, and sealing means at the periphery of said shaped surface adaptedto engage the base of said generally frusto-conical body to seal thespace within said frusto-conical body from the external space thereof atsaid periphery, means closing the die adjacent said periphery to formthereby a fluid tight container, and means for supplying high pressurefluid to the space within said frusto-conical body to cause stretchingthereof to move it into contact with said shaped surface.

7. The method for forming semi-elliptical head closures for pressurevessels having a central opening on the minor axis of the ellipse, froma flat body of hard-to-work thin sheet metal, which method comprises:deforming said flat sheet metal body into a hollow frustum of a conehaving a wall thickness equal to the desired thickness of thesemi-elliptical head closure, and having open ends; inserting saidfrustum of a cone into a die having the desired semi-ellipsoidal shape;sealing the joint between said frustum of a cone and said die; and thendeforming said frustum of a cone into the desired semi-elliptical headclosure, by stretching by fluid pressure said frustum of a conecircumferentially in the set of planes of its original curvature only,until said frustum of a cone conforms to the shape of said die.

8. The method as defined by claim 7, in which the stretching of thefrustum of a cone occurs only circumferentially, with freedom of motionof the frustum of a cone parallel to the minor axis of saidsemi-ellipsoidal die.

9. The method as defined by claim 7 characterized by the use of afrustum of a cone having cambered walls, the amount of camber beingpredetermined to compensate for local thinning of metal when stretched.

10. The method as defined by claim 7 characterized by the use of afrustum of a cone having variable wall thickness.

11. The method for forming hemi-spherical head closures for pressurevessels having a central opening on the longitudinal axis, from a flatbody of hard-to-work thin sheet metal, which method comprises: deformingsaid flat sheet metal body into a hollow frustum of a cone having a wallthickness equal to the desired thickness of the hemi-spherical headclosure, and having open ends; inserting said frustum of a cone into adie having the desired hemi-spherical shape; sealing the joint betweensaid frustum of a cone and said die; and then deforming said frustum ofa cone into the desired hemi-spherical head closure, by stretching byfluid pressure said frustum of a cone circumferentially in the set ofplanes of its original curvature only, until said frustum of a coneconforms to the shape of said die.

12. The method as defined by claim 11 in which the stretching of thefrustum of a cone occurs only circumferentially, with freedom of motionof the frustum of a cone parallel to the symmetrical axis of saidhemi-spherical die.

13. The method as defined by claim 11 characterized by the use ofcambered walls, the amount of camber being predetermined to compensatefor local thinning of the metal when stretched.

14. The method as defined by claim 11 characterized by the use of afrustum of a cone having variable wall thickness.

15. The method of claim 1, said shaped curved surface includingcurvature in said first mentioned set and also including curvature inthe other of said two sets.

16. The method for forming bodies having compound curvature, whichmethod comprises forming a first flat body into a first curved preformbody having curvature in only one set of at least two sets of transverseparallel planes; forming a second fiat body into a second curved preformbody having curvature in said only one set; positioning each of saidcurved preform bodies in 2. respective die, each of said dies having ashaped compound curved surface including curvature in said only one setand also including curvature in the other of said two sets; juxtaposingsaid dies so that said curved preform bodies face each other and providea joint therebetween; sealing said joint; and stretching both of saidcurved preform bodies simultaneously, but each only in said only one setof planes, into contact with said shaped compound curved surface of therespective dies, to shape the curved preform bodies to the curvature ofsaid compound curved surfaces, by increasing fluid pressure between saidcurved preform bodies.

17. The method for forming a desired thin-walled body of compoundcurvature from a flat body of hard-to-Work thin sheet metal, whichmethod comprises: deforming said fiat sheet metal body into a preformbody approximating a frustum of a cone in shape and also approximatingthe shape of the desired body of compound curvature; inserting saidfrusto-conical preform body into a die having a central axis and alsohaving a shaped curved surface which corresponds to the shape of thedesired body of compound curvature and has been generated by rotating acurved line about said central axis, said shaped curved surfaceincluding curvature in the same set of planes as said frustoconicalpreform body; sealing the joint between said frusto-conical preform bodyand said die; and, then deforming said frusto-conical preform body intothe desired thin-walled body of compound curvature, by expanding saidpreform body by fluid pressure in the set of planes of its originalcurvature only, to impart curvature in said preform body in the other ofsaid sets, until said body conforms to said shaped curved surface.

References Cited in the file of this patent UNITED STATES PATENTS938,816 Bourgeois Nov. 2, 1909 939,702 Jones Nov. 9, 1909 1,329,969Harrison Feb. 3, 1920 2,038,304 Middler Apr. 21, 1936 2,086,134 LudwickJuly 6, 1937 2,317,869 Walton Apr. 27, 1943 2,498,275 Johnson Feb. 21,1950 2,503,191 Branson Apr. 4, 1950 2,579,646 Branson Dec. 25, 19512,675,608 Vines Apr. 20, 1954 2,696,184 Demarest Dec. 7, 1954 2,752,675Bauer July 3, 1956 2,763,917 Huet Sept. 25, 1956 2,763,924 BellomettiSept. 25, 1956 2,841,865 Jackson July 8, 1958 2,849,977 Nielsen Sept. 2,1958 2,861,530 Macha Nov. 25, 1958 FOREIGN PATENTS 451,056 Italy Aug.23, 1949

1. THE METHOD FOR FORMING A DESIRED THIN-WALLED BODY OF COMPOUNDCURVATURE FROM A FLAT BODY OF HARD-TO-WORK THIN SHEET METAL, WHICHMETHOD COMPRISES: DEFORMING SAID FLAT SHEET METAL BODY INTO A CURVEDPERFORM BODY APPROXIMATELY THE SHAPE OF THE DESIRED BODY OF COMPOUNDCURVATURE AND HAVING A CURVATURE IN ONLY ONE OF AT LEAST TWO SETS OFTRANSVERSE PARALLEL PLANES; INSERTING SAID PERFORMED BODY INTO A DIEHAVING A CURVED SURFACE CORRESPONDING TO THE DESIRED BIDY OF COMPOUNDCURVATURE; SEALING THE JOINT BETWEEN SAID PREFORM BODY AND SAID DIE; ANDTHEN DEFORMING SAID CURVED